Question

Aman invested a sum of Rs.P for 2 years at 12% p.a. compound interest and received some interest. Ajay invested Rs.(P+3000) for 3 years at 8% p.a simple interest and received the interest same as received by Aman. The sum invested by Aman is:

• A. Rs.25,000
• B. Rs.50,000
• C. Rs.65,000
• D. Rs.60,000

Hint:

For compound interest over two years, the effective interest rate is \( (2R + R^2/100)% \). For Aman, this is \( (2 \times 12 + 144/100) = 24 + 1.44 = 25.44% \). For simple interest, the rate is just \( R \times T \), which for Ajay is \( 8 \times 3 = 24% \).

Answer 1

The Correct Option is B

Step 1: Calculate the compound interest (CI) earned by Aman. The formula for the amount A is \( A = P(1 + R/100)^T \). Aman's Amount = \( P(1 + 12/100)^2 = P(1.12)^2 = 1.2544P \). Aman's Interest = Amount - Principal = \( 1.2544P - P = 0.2544P \).

Step 2: Calculate the simple interest (SI) earned by Ajay. The formula for Simple Interest is \( SI = (P \times R \times T)/100 \). Ajay's Interest = \( \frac{(P+3000) \times 8 \times 3}{100} = \frac{24(P+3000)}{100} = 0.24(P+3000) = 0.24P + 720 \).

Step 3: Equate the two interests and solve for P. Given that the interests are the same: \[ 0.2544P = 0.24P + 720 \] \[ 0.2544P - 0.24P = 720 \] \[ 0.0144P = 720 \] \[ P = \frac{720}{0.0144} = \frac{7200000}{144} = 50,000 \] The sum invested by Aman (P) is Rs.50,000.